Compositor has a different effect when editing Render Result vs external PNG image?
This issue is that the exported image has been conveted using color management transforms.

In short words, the renderer will determine a light value for each pixel, with range from 0 to infinity in a linear way. When you export an image every value will be converted to fit the 0.0 (black) - 1.0 (white) range, and applies a transform, determined by the settings on the color management section.

The values of the two images (rendered and exported) will be different. In other words: the original values are unbound and linear (also known as Scene Referred), the values on a PNG are limited and a "gamma curve" has been applied so the values are no longer linear (they have been converted to Display Referred)

See this answer for more detailed infos Render with a wider dynamic range in cycles to produce photorealistic looking images. 

Saving the image as EXR files, will allow you to retain the original unbound and linear light values!